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Datatype-Generic Programming ; International Spring School, SSDGP 2006, Nottingham, UK, April 24-27, 2006, Revised Lectures
A leitmotif in the evolution of programming paradigms has been the level and extent of parametrisation that is facilitated — the so-called genericity of the paradigm. The sorts of parameters that can be envisaged in a programming language range from simple values, like integers and fioating-point numbers, through structured values, types and classes, to kinds (the type of types and/or classes).Datatype-generic programming is about parametrising programsby the structure of the data that they manipulate. To appreciate the importance of data type genericity,one need look no further than the internet. The internet is a massive repository of structured data, but the structure is rarely exploited. For example, compression of data can be much more efiective if its structure is known, but most compression algorithms regard the input data as simply a string of bits, and take no account of its internal organisation. Datatype-generic programming is about exploiting the structure of data when it is relevant and ignoring it when it is not. Programming languages most c- monly used at the present time do not provide efiective mechanisms for do- menting and implementing datatype genericity.
Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra
This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory.
Column Generation
Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).
Linear Programming : Foundations and Extensions
Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail.
Languages and Compilers for Parallel Computing ; 21th International Workshop, LCPC 2008, Edmonton, Canada, July 31 - August 2, 2008, Revised Selected Papers
This book constitutes the thoroughly refereed post-conference proceedings of the 21th International Workshop on Languages and Compilers for Parallel Computing, LCPC 2008, held in Edmonton, Canada, in July/August 2008.The 18 revised full papers and 6 revised short papers presented were carefully reviewed and selected from 35 submissions. The papers address all aspects of languages, compiler techniques, run-time environments, and compiler-related performance evaluation for parallel and high-performance computing and comprise
C# 10 Quick Syntax Reference : A Pocket Guide to the Language, APIs, and Library
Reviews the essential C# 10 and earlier syntax, not previously covered, in a well-organized format that can be used as a handy reference. Specifically, unions, generic attributes, CallerArgumentExpression, params span, Records, Init only setters, Top-level statements, Pattern matching enhancements, Native sized integers, Function pointers and more. You will: Employ nullable reference types / Work with ranges and indices / Apply recursive patterns to your applications / Use switch expressions
Binary Quadratic Forms: An Algorithmic Approach
This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography.
Arithmetical investigations : Representation theory, orthogonal polynomials, and quantum interpolations
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Analytic Number Theory : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 11-18, 2002
The four contributions collected in this volume deal with several advanced results in analytic number theory. Friedlander’s paper contains some recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials. Heath-Brown's lecture notes mainly deal with counting integer solutions to Diophantine equations, using among other tools several results from algebraic geometry and from the geometry of numbers. Iwaniec’s paper gives a broad picture of the theory of Siegel’s zeros and of exceptional characters of L-functions, and gives a new proof of Linnik’s theorem on the least prime in an arithmetic progression. Kaczorowski’s article presents an up-to-date survey of the axiomatic theory of L-functions introduced by Selberg, with a detailed exposition of several recent results.
An Introduction to Number Theory
An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject. In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory. A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography.
Algorithms – ESA 2005 ; 13th Annual European Symposium, Palma de Mallorca, Spain, October 3-6, 2005, Proceedings
This volume contains the 75 contributed papers and the abstracts of the threeinvited lectures presented at the 13th Annual European Symposium on Algo-rithms (ESA 2005), held in Spain, 2005. respectively.Papers were solicited in all areas of algorithmic research, including but notlimited to algorithmic aspects of networks, approximation and on-line algo-rithms, computational biology, computational geometry, computational financeand algorithmic game theory, data structures, database and information re-trieval, external memory algorithms, graph algorithms, graph drawing, machinelearning, mobile computing, pattern matching and data compression, quantumcomputing, and randomized algorithms. The algorithms could be sequential,distributed, or parallel. Submissions were especially encouraged in the area ofmathematical programming and operations research, including combinatorialoptimization, integer programming, polyhedral combinatorics, and semidefiniteprogramming.Each extended abstract was submitted to one of the two tracks.
Algèbre, Chapitres 1 à 3 = Algebra, Chapters 1 to 3
To do algebra is essentially to calculate, that is to say to perform, on elements of a set, (<algebraic operations n, the best-known example of which is provided by the (<four rules)) of elementary arithmetic. This is not the place to retrace the slow process of progressive abstraction by which the notion of algebraic operation, initially restricted to natural integers and to measurable quantities, gradually widened its field, as it grew. at the same time generalized the notion of ((number O, until, going beyond the latter, it came to apply to elements which no longer had any character ((numeric)>, for example to permutations of a - seems (see Historical Note in chap. 1).
Algèbre commutative : Chapitres 5 à 7 = Commutative algebra : Chapters 5 to 7
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations.This second volume of the Book of Commutative Algebra, Seventh Book of the treatise, introduces two fundamental notions in commutative algebra, that of algebraic integer and that of valuation, which have many applications in number theory and algebraic geometry.
